Abstract

In the frame of non‐relativistic quantum mechanics we discuss the systems of N particles, whose energy is close to that of the dissociation threshold. We show that in systems, where a long‐range repulsion acts between the dissociation fragments, there is a super‐size blocking, i.e. the halo structures in these systems do not appear. We discuss the connection between bound states at the threshold and spreading and derive the conditions on pair potentials, which guarantee the super‐size blocking. Under minor assumptions we prove that negative atomic ions have a bound state at the threshold when the charge of the nucleus is critical.